Analyzing the Influence of Induction Machine Design on Transient Slot Leakage Inductance with respect to Sensorless Rotor Position Estimation

Transcription

1 Analyzing the Influence of Induction Machine Design on Transient Slot Leakage Inductance with respect to Sensorless Rotor Position Estimation M.A. Samonig 1 and T.M. Wolbank 1 1 Vienna University of Technology, Department of Energy Systems and Electrical Drives, Vienna, Austria Abstract The paper analyzes the transient reaction of squirrel cage induction machines to voltage step excitation. The involved excitation technique uses the drive s inverter to excite the machine with voltage steps. The transient nature of these steps demands high flux linkage derivatives. In response, the squirrel cage acts as a barrier hindering the flux to penetrate the rotor yoke and forcing it into the air gap. Thus, the stator winding is linked to pure leakage flux, composed of slot and zig-zag leakage. A turning rotor modulates these flux components by changing the machine s magnetic permeances. Since these modulations are linked to the rotor slotting, they may be exploited to derive a rotor position signal. Understanding and predicting them is the key to assess different IM designs with respect to their applicability for sensorless position estimation. The investigation methodology used includes analytical modelling and finite element simulations, confirming the results of each other. Finally, different design variations are assessed. Keywords transient magnetic flux leakage, analytical model, numerical simulation I. INTRODUCTION A widely used sensorless position estimation concept is based on the tracking of saliency dependent stator inductance variations. These variations can be exploited by establishing a high frequency or transient voltage excitation of the machine and measuring the current response. The techniques used to excite the machine can be classified into two groups: a. High frequency or transient signal injection in addition to the fundamental wave. b. PWM-integrated silent methods. Group a) either applies periodic [1]-[6] or transient test voltage signals [7]-[10], making use of rotating and pulsating waveforms or applying dedicated switching patterns. However, additional signal injection may influence inverter switching frequency and give rise to unfavorable effects like: acoustic noise emissions, decreased maximum inverter output voltage or additional current ripple. In order to reduce these drawbacks recent scientific research is focused at excitation techniques belonging to group b). The aim is to integrate the transient The authors want to thank Bombardier Transportation (RoQ) and especially Heiko Mannsbarth, Markus Jörg, Martin Bazant and Markus Vogelsberger for the generous support and cooperation. excitation sequences into the PWM-sequence used for fundamental wave excitation, [10]-[13]. Since the stator inductance variations exploited by these methods originate from machine slotting and saturation, they can be used to estimate rotor and flux position, respectively. However, to keep the focus on the rotor slotting saliency, in this paper induction machines (IM) are analyzed without fundamental wave excitation. This means there are no saturation effects and no intermodulation between rotor slotting and saturation harmonics. However, as was already shown in literature, the dominant rotor slotting harmonic is not influenced by machine main flux saturation. Saturation saliency acts as an additional disturbance signal, without influencing slotting itself. Thus, results obtained are valid also with additional saturation saliency present in the machine. Goals of the paper are: 1. Analyzing the relationship between IM design (i.e. slot number, short-pitching) and rotor slotting signals (occurrence, magnitude) with a combination of numerical finite element (FE) simulations and analytical model (AM). 2. Evolving the analytical model to the point where it allows for prediction of the signal magnitudes of more complex design variations (short-pitching), without the need of timeconsuming FE simulations. 3. Developing simple IM design rules in order to predict the occurrence of slotting signals for any combination of stator/rotor slots and winding configuration, e.g. short-pitching. As shown in the following, the results of FE model and AM are in agreement with each other. Thus, their comparison may and will be used as an additional form of validation, since the FE results have already been supported by measurements in previous investigations [14]. Different from the applicationoriented investigations for a single test machine in [15], this paper is focused on a generalized formulation and prediction of slotting related effects in a variety of machine designs. II. TRANSIENT LEAKAGE FLUX A. Single current-carrying slot Results presented in the following are applicable for all groups of excitation methods (a, b) that rely on voltage steps (inverter switching). However, with some minor adjustments they should be valid for other high-frequency excitations as /17/$ IEEE

2 well. The transient nature of the involved pulses or steps generated by the inverter demands high flux linkage timederivatives. In response, the squirrel cage acts as a barrier hindering the flux to penetrate the rotor yoke and forcing it into the air gap, see Fig. 1. slot-slot slot-tooth Fig. 1: Only middle slot carries a winding. Left: Squirrel cage forces flux into airgap. Stator slot opposed to rotor slot (slot-slot position). Right: Changed flux distribution due to new rotor position (slot-tooth), where stator slot is opposed to rotor tooth. (Note: Flux line plots based on FE simulation results.) In the figures above, only one slot carries a winding. Nonetheless, the principle of transient flux expulsion can clearly be seen, which exposes the resulting flux as pure leakage flux. Furthermore, two components can be identified: slot leakage flux (passing the stator slot area) and zig-zag flux (alternating via the air gap between stator and rotor). In the following the sum of these two components will be referred to as transient (index t) inductance. Assuming open or semi-closed stator slots, this transient inductance varies dependent on the rotor position. It is minimum for slot-slot and maximum for slot-tooth positions, see Fig. 1 left and right, respectively. According to (1) the corresponding slot current derivatives vary inversely proportional to, since the exciting voltage pulse height (= DC link voltage) is kept constant. This gives maximum for slot-slot and minimum for slot-tooth positions. = = (1) In this equation, the voltage imposed on the winding resistance is not included, because it is insignificant compared to the DC link voltage. As mentioned in the introduction, no fundamental wave excitation is considered, thus the back emf term is also neglected. Equation (1) also shows, that measurement of the phase current responses allows for monitoring of the transient inductance change. In turn this may be used to derive the rotor position. Due to its fundamental importance, investigations on this transient (slot) inductance will be focus of the following sections. The first step is only summarized here, though. It included calculation of from the simulations corresponding to Fig. 1. The finding was, that the transient inductance for changing rotor position varies with a sinus-like function (deviations negligible). Thus it has been assumed, that the inductance modulation may be approximated with a sinusoidal function. As will be shown in the next section, this approximation is still valid if the stator slots carry a complete phase winding. B. Complete phase winding Investigations in the previous section suggested to approximate the transient inductance modulation by a sinusoidal function. This idea is illustrated by the schematic in Fig. 2. The figure shows the relative position of stator and rotor (initial rotor position). It can be seen, that stator slots 1, 2 and 3 are opposed to different rotor parts. Slot 1 is opposed by a rotor slot, slot 2 by a tooth-tip and slot 3 by a rotor tooth. It is clear that these different situations represent varying magnetic permeances for the zig-zag leakage component. For example, the rotor tooth in opposition to slot 3 is composed of iron material. This means, the magnetic permeance (= ability to carry magnetic flux) of the zig-zag path is maximum. This goes along with maximum transient inductance related to slot 3. Consequently, slot 1 is in a minimum inductance position, since the zig-zag flux has to pass a rotor slot opening. The periodicity of this permeance modulation is dependent on the rotor design, i.e. the number of rotor slots N R. Thus, the period is one rotor slot pitch (RSP) and the phase shift between adjacent slots depends on the difference between N R und the number of stator slots N S. Fig. 2: Relative stator and rotor slot positions and approximated inductance levels. First 3 slots of full-pitch stator winding of phase L1 (number of slots/pole/phase q=3). Stator slot pitch (SSP), rotor slot pitch (RSP). Same must be true for the actual transient inductance modulation, as proven by the FE simulation results in Fig. 3. Fig. 3: Simulated inductance modulations of the 3 slots in Fig. 2, when rotor is rotated by one rotor slot pitch (RSP) in clockwise direction. Line style indicates layer. Initial sampling locations of the sinusoidal inductance approximation are marked with x. Initial stator/rotor position according to Fig. 2. The figure shows the variation of the transient inductance during a rotor movement equivalent to one RSP. The plotted

3 courses represent upper and lower layers of the same winding phase L1. Both layers of one slot show nearly the same modulation magnitude and phase, but different average values. This difference comes from the fact that the lower layer is linked to both leakage fields, its own as well as the one of the upper layer. Therefore, its average inductance is slightly bigger. The FE results confirm the applicability of the sinusoidal approximation. III. ANALYTICAL MODEL In the following chapter the analytic approximation of the transient inductance, comprising slot and zig-zag leakage, is summarized. Considerations begin with general formulations of the slot leakage inductance, as given in [16] or [17]. A. Conventional slot leakage calculation The chosen formulation is based on the calculation of the flux Ψ linked to the winding parts located in a given slot. However, differently from the conventional approach not only the slot leakage flux Ψ, but also the zig-zag part Ψ is considered in the transient case. Division by the excitation current gives the corresponding transient leakage inductance. = Ψ = Ψ + Ψ (2) In order to simplify the analysis following assumptions are made (cp. Fig. 4): infinitely permeable iron region (µ r ), slot walls considered parallel, slot width b slot small compared to height h slot, semi-closed slots. In this case the magnetic slot field may be approximated by its orthogonal component alone and the rotor position dependent zig-zag flux modulation is facilitated. The slot shape of Fig. 1 supports this assumption quite well, although the slot dimensions differ from the simplified rectangular case depicted in Fig. 4. Fig. 4: Possible conventional slot leakage flux paths (full lines) in case of a double layer stator winding. Slot leakage flux stays at the stator side, whereas zig-zag flux leakage paths (dashed lines) are moving back and forth between stator and rotor. The zig-zag flux paths vary for slot-slot and slot-tooth position. With these simplifications and dimensions (Fig. 4) Ampere s law is used now to calculate the magnetic field intensity in the slot and air gap regions, where i(y) represents the accumulated current linkage starting from the slot ground. ( ) = ( ) ( )/ ( ) (3) The variable b(y) gives the altering slot width along the axis y. In turn this allows for determination of the slot flux density ( ). Integration along the axis and multiplication by the machine axial length gives the flux value Φ: Φ=( ) = ( ), (4) where is the permeability of free-space and [h a, h b] specifies the integration interval (intervals of constant width). Finally, the leakage flux linkage calculation considers that not all winding turns are linked to the same amount of flux, but the number of linked turns ( ) is increasing with position within the slot. Ψ=( ) ( ). (5) In order to determine mutual and self-inductance values, the upper and lower layer winding in turns are excited by a current. The exact procedure and derivation of functions ( ) and ( ) can be found in literature (e.g. [16]). In the following only the results for upper (index u) and lower (index l) layer s self and mutual (index m) flux linkages are shown. The corresponding variables are Ψ, Ψ, and Ψ, respectively. Ψ, = 1 h /2 3 Ψ, = 1 h /2 /2 3 Ψ = 1 2 h /2 W represents the number of coil turns. The ratios in brackets are dependent on the slot geometry (height and width) and define the well-known magnetic permeance factors. Furthermore, it is assumed, that the same current i is flowing in upper and lower layer of each slot, i.e. a full-pitch (diameter) winding is used. The general case of short-pitched windings featuring different layer currents in one slot, will be addressed later. In the next section the focus is laid on extending the conventional formulation with the zig-zag leakage component. B. Considering zig-zag leakage The second share in the overall transient leakage flux is represented by paths alternating between stator and rotor. It is thus called zig-zag flux and may be included in the calculation by considering the corresponding air regions along its way. From Fig. 4 these regions can be identified as two air gap crossings and, dependent on the rotor position, up to one additional crossing of the rotor slot opening. A slot-slot position thus gives the minimum slot leakage inductance (max. length of air path), whereas a slot-tooth opposition corresponds to maximum leakage inductance (max. iron influence). This results in the distinct transient leakage inductance modulation already shown in Fig. 1. The involved permeance factors are: (6) = and =, (7)

4 (cross section divided by length along flux paths). Since these permeances are connected in series (two airgap crossings) the complete zig-zag permeance factor becomes: = (8) h The right part of this equation gives approximations for the two relative slot positions (slot-slot, slot-tooth). Finally, the permeance factor is added to the brackets of (6). Ψ, = 1 h /2 3 Ψ, = 1 h /2 /2 3 Ψ = h /2 + The sum of self and mutual slot flux linkages finally gives the results for upper and lower layer winding parts, from which the transient leakage inductance may be calculated. =, + =,, +, =, =, + =,, +, =,,, +, =,,, +, =, (9) (10) As already mentioned, a full-pitch (diameter) winding is assumed here, i.e. the same current i is flowing in upper and lower layer of each slot. = =, (11) The general case of a short-pitched winding featuring different layer currents in one slot is addressed in the following. C. Considering short-pitching The introduction of short-pitching reduces the span of each winding coil. The initial coil span of one pole pitch (full-pitch) is shortened in steps of one stator slot pitch (SSP). This equals a relative shift of upper and lower layer by a certain amount of SSP. Consequently, short-pitching introduces stator slots carrying conductors of different phases. The currents and thus are different for upper and lower layer in these slots. This must be considered in (10) and gives: =, + =,, +, (12) =, + =,, +,. For example, in case of a symmetrical star connected winding and pulsed excitation in direction of phase L1, the phase currents show the following relation: = and = =. (13) If a slot now carries an upper layer belonging to phase L1 and a lower layer belonging to L2, the upper layer flux linkage of (12) becomes: =,, +, =(,, +, ) =,, (14) (,, +, )=,. Compared to (10), the influence of the mutual transient inductance, is lowered by a factor in case of this layer combination. Similar factors can be found for all possible combinations and winding connections (star, delta). However, this is not shown here and can be found in literature (e.g. [16]). In the following only the results obtained with the derived analytical model are presented and compared to FE simulations. The used winding parameters are: 3-phase (m = 3), 4 series-connected poles (p = 2), distributed (slots per pole and phase q = 3), star connection. I. ANALYTICAL MODEL VS. FE MODEL If the analytical calculation outlined is executed, the magnitude of the transient leakage inductance may be derived. Adding these values up considering the phase shift between adjacent slots (cp. Fig. 2, shift becomes zero if N S = N R), the transient inductance of the whole stator winding can be determined. A convenient way to achieve this is by representing the momentary (for given rotor position) slot inductance values of Fig. 3 by phasors in the complex plane (inductance phasors), see Fig. 5. Fig. 5:Phasor diagram representing the momentary leakage inductance values in Fig. 2 (initial rotor position). Slot numbers according to Fig. 2, average values not considered. (N S = 36, N R = 44) With this representation, it is possible to approximate the rotor slot dependent transient inductance modulation experienced by the stator winding. In order to prove the approximation accuracy, Fig. 6 shows a comparison between simulated (FE, black) and calculated (AM, grey) slotting signal magnitudes. Note, that these results represent the transient inductance of a complete three-phase stator winding composed of the single slot inductances. Modulation [μh] N S < N R < 1.25N S Rotor Slot Number N R Fig. 6: Comparison of transient inductance magnitudes of whole three-phase winding determined with analytical model (grey, right) and with FE simulation (black, left). Design parameters N S=36, p=2 (pole-pair number) and m=3 (number of phases) are kept constant, whereas N R is varied. The results are in good agreement with the FE simulation and confirm the validity of the model approach. This is FE AM

5 especially true for commonly applied N S-N R combinations (0.75N S < N R < 1.25N S). Rotor slot numbers out of this range introduce additional losses, asynchronous torques, etc. In fact, the rotor slot number (N R = 20) showing the highest mismatch to FE simulation results is outside of this range. Nevertheless, the deviation of about 40% is quite remarkable. This deviation is probably introduced by the fact that an additional flux linkage redistribution occurs when the rotor is turned. This effect is inherently considered by the FE model but not by the AM. Furthermore, machines featuring N S=N R=36 are usually not applied in practical operation due to their synchronous torques at standstill. However, they may serve as a reference to assess other combinations in the following. I. COMPARISON OF DIFFERENT DESIGNS As shown in the previous chapters, the proposed inductance phasor representation may be used to understand and predict the transient slotting signal of different machine designs. From this analysis, simple rules can be derived, allowing the assessment of IM design with respect to sensorless rotor position estimation. A. Design variation: p-n R relation As an example, the diagram of Fig. 6 is taken and compared to selected inductance phasor diagrams in Fig. 7. Not surprisingly, the maximum inductance modulation is present in the machine featuring N S=N R=36. The corresponding inductance phasors of all slots (only slots 1, 2 and 3 depicted) are in phase. As already mentioned, such a design is usually not realized in practical operation. However, it may serve as a reference to assess the other combinations. Moving away from N S=N R, i.e. increasing or decreasing N R, reduces the slotting modulation magnitude. The reduction is somewhat bigger for N R>N S. This is due to the increase in the number of rotor slots, comparable to a reduced influence of the iron. A special case is given at N R=24, where the slot inductance phasors are symmetrical ( coil side symmetry ) and cancel each other out. Modulation [μh] cancelation 2p 2p m 2p Rotor Slot Number N R Fig. 7: Lower: Transient inductance magnitudes (whole winding) for different machine designs. Winding configuration (full-pitch) and parameters N S=36, p=2 and m=3 are kept constant, whereas N R is varied. Upper: Inductance phasor diagrams as derivable from both models (FE and AM), featuring the first three stator slots (cp. Fig. 2) of two different designs. 2p FE AM Simple design rules may be derived from Fig. 7. Rotor slotting modulations are only visible with designs featuring rotor slot numbers N R that are integer multiples of the pole number 2p. =2 (15) = 0, 1, 2, 3, IM designs complying with this rule are likely to deliver rotor slotting modulations exploitable for sensorless position estimation. However, as shown in Fig. 7, exceptions do exist. These are namely the p-n R relations causing coil side symmetry. In this cases N R is divisible by 2p m without remainder, but the slotting modulation is likely to be very small. Consequently, it is difficult to apply such designs in combination with sensorless position estimation. In fact, the resulting p-n R relationship (15) is similar to the necessary condition for the occurrence of principal slot harmonics in line current based techniques, which apply machine current signature analysis (MCSA). =2 3( ) ] (16) = 0, 1, 2, 3, ; = 0 1 Derivation of this equation can be found e.g. in [18] and [19]. Although it looks more complex for MCSA than for transient pulse excitation, it delivers the same N R results. B. Design variation: short-pitching In order to show the combined influence of short-pitching and rotor slot on the rotor slotting signal magnitude, different test machine setups were analyzed analytically. During these investigations only short-pitching and rotor slot number were varied. Other machine parameters relating to geometry and winding were not changed. The analytical findings were also compared to FE simulations. Since deviations again were small, only analytical results are given in the following. Similar to the full-pitch winding in Fig. 7, the transient inductance modulation in Fig. 8 periodically decreases/increases its magnitude if the rotor slot number is changed, starting from N R = N S (= 36). However, the period of this change is also influenced by the short-pitching ratio. This is most clearly visible for N R = 24 and 8/9 (also 7/9), where the rotor slotting harmonic is no longer zero compared to the fullpitch winding (9/9). short-pitching: 9/9 8/9 7/9 6/9 sensitive to variation 1000 Modulation [μh] Rotor Slot Number N R Fig. 8: AM results: Inductance modulation magnitude of neutral point winding for varying number of rotor slots and short-pitching ratio. With N S = 36 and p = 2, this gives pitching in steps of 1/9 (i.e. from left to right: 9/9, 8/9, 7/9 and 6/9). In the practically relevant range of rotor slot numbers (0.75N S < N R < 1.25N S) N R = 28 and 44 are most sensitive to short-pitching variations. Both show the same ratio between

6 maximum (9/9) and minimum (7/9) modulation magnitudes. Again, inductance magnitudes are reduced in case of N R = 44 (compared to N R = 28), due to the increase in the number of rotor slots. The same effect can be seen when comparing N R = 32 and 40. However, these two designs show minimum sensitivity. Therefore, good accuracy of rotor position estimation performance can be expected using these combinations even if a short-pitched winding is used. II. CONCLUSION A simple analytical model has been developed and compared to FE simulations. It has been shown, that this model is capable of predicting the transient leakage inductance variations related to rotor slotting of squirrel cage IM. The presented results were used to prove that only certain pole and rotor slot number combinations exhibit rotor slotting harmonics under transient pulse excitation. The identified necessary conditions are similar to the ones related to principal slot harmonics in current signature based techniques. Furthermore, the analytical model was used to investigate the influence of short-pitching on the slotting harmonic magnitude. It has been shown that certain designs react more sensitive to such variations than others. Compared to time-consuming finite element simulations, the presented model can be used as a fast way to predict the performance of induction machine designs with respect to transient (and high-frequency) saliency based sensorless position estimation. REFERENCES [1] D. Reigosa, F. Briz, C. Blanco, J.M. Guerrero, Sensorless Control of Doubly-Fed Induction Generators Based on Stator High Frequency Signal Injection, IEEE Transactions on Industry Applications, Vol. 50, Issue. 5, pp , [2] D. Reigosa, P. García, F. Briz, D. Raca and R.D. Lorenz, Modeling and adaptive decoupling of transient resistance and temperature effects in carrier-based sensorless control of PM synchronous machines, IEEE Trans. Ind. Appl., Vol. 46 (1), pp , [3] N. Teske, G.M. Asher, M. Sumner and K.J. Bradley, Analysis and Suppression of High Frequency Inverter Modulation on Sensorless Position Controlled Induction Machine Drives, IEEE Transactions on Industry Applications, Vol. 39, no. 1, pp , (2003) [4] A. Consoli, G. Scarcella and A. Testa, A New Zero-Frequency Flux- Position Detection Approach for Direct-Field-Oriented- Control Drives, IEEE Transactions on Industry Applications, Vol. 36, no. 3, pp , (2000) [5] Q. Gao, G. M. Asher and M. Sumner, Sensorless Position and Speed Control of Induction Motors Using High Frequency Injection and Without Offline Precommissioning, IEEE Transaction on Industrial Electronics, Vol. 54 pp , (2007) [6] J. Ha, S.K. Sul, Sensorless Field Orientation Control of an IM by High Frequency Signal Injection, IEEE IAS Annual Meetg., pp , (1997) [7] J. Holtz, H. Pan, Elimination of Saturation Effects in Sensorless Position Controlled Induction Motors, IEEE IAS Annual Meetg., Vol3, pp , (2002) [8] C. Spiteri, Staines, G.M. Asher and M. Sumner, Sensorless Control of Induction Machines at Zero and Low Frequency using Zero Sequence Currents, IEEE Transactions on Industrial Electronics, vol.53, no.1, pp , (2005) [9] M. Schroedl, Sensorless Control of Ac Machines at Low Speed and Standstill Based on the INFORM Method, Industry Applic.Conf.(IAS), pp (1996) [10] D. Paulus, P. Landsmann, R. Kennel, General arbitrary injection approach for synchronous machines, IEEE International Symposium on Sensorless Control for Electrical Drives and Predictive Control of Electrical Drives and Power Electronics (SLED/PRECEDE), pp. 1-6, 2013 [11] Q. Gao, G.M. Asher, M. Sumner and P. Makys, Position Estimation of AC Machines Over a Wide Frequency Range Based on Space Vector PWM Excitation, IEEE Transactions on Industry Applications, vol. 43, no. 4, pp , (2007) [12] J. Holtz, J. Juliet, Sensorless acquisition of the rotor position angle of induction motors with arbitrary stator windings, IEEE Transactions on Industry Applications, vol.41, no.6, pp , (2005) [13] P. Nussbaumer, Th.M. Wolbank, Using Switching Transients to Exploit Sensorless Control Information for Electric Machines, Symposium on Sensorless Control for Electrical Drives (SLED), pp , 2011 [14] M.A. Samonig, Th.M. Wolbank, Prediction of Slotting Saliency in Induction Machines with Respect to High-Frequency-Excitation Based Sensorless Control, Proceedings of Conference on IEEE Industrial electronics Society (IECON), 2014 [15] M. Amhof; M.A. Samonig, Th.M. Wolbank, Sensorless position estimation from PWM-induced transient excitation in induction machines, 41st Annual Conference of the IEEE Industrial Electronics Society (IECON), pp , (2015) [16] E. Bolte, Elektrische Maschinen Grundlagen, Magnetfelder, Wicklungen, Asynchronmaschinen, Synchronmaschinen, Elektronisch kommutierte Gleichstrommaschinen, (transl. Electrical Machines Basics, Magnetic fields, Windings, Induction machines, Synchronous machines, Electrically commutated DC machine), ISBN , Springer-Verlag, Berlin Heidelberg (2012) [17] A. Cavagnino, On the Accuracy of the Slot Leakage Inductance Analytical Computation, Proceedings of XXII International Conference on Electrical Machines (ICEM), 2016 [18] A. Ferrah, P.J. Hogben-Laing, K.J. Bradley, G.M. Asher and M.S. Woolfson, The Effect of Rotor Design on Sensorless Speed Estimation Using Rotor Slot Harmonics Identified by Adaptive Digital Filtering Using The Maximum Likelihood Approach, 32 nd IEEE IAS Annual Meeting, New Orleans, vol.1, pp , (1997). [19] S. Nandi, H.A. Toliyat, Detection of Rotor Slot and Other Eccentricity Related Harmonics in a Three Phase Induction Motor with Different Rotor Cages, International Conference on Power Electronic Drives and Energy Systems for Industrial Growth, vol.1, pp , (1998).